1. Field of the Invention
The present invention relates to an exposure apparatus and a method of manufacturing a device.
2. Description of the Related Art
A projection exposure apparatus has conventionally been employed to manufacture devices such as a semiconductor device by using photolithography. The apparatus projects and transfers a circuit pattern formed on a reticle (mask) onto a photoresist, which is applied on, for example, a wafer, by a projection optical system.
The projection optical system of the projection exposure apparatus is regulated or adjusted by a process of measuring the optical characteristics (e.g., various aberrations) of the projection optical system, a process of calculating a regulation amount (correction amount) for regulating the optical characteristics based on their measurement values, and a process of regulating the projection optical system based on the calculated regulation amount.
Most optical characteristics (e.g., various aberrations) to be regulated change in proportion to the regulation amount of each element (e.g., an optical element such as a lens), and their absolute values are required to be minimized. To meet this demand, Japanese Patent Laid-Open No. 2002-367886 proposes a technique of determining the regulation amount of each element using the linear programming.
The optical characteristics to be regulated include characteristics, such as the square of the RMS (root mean square) value of the wavefront aberration, which are expressed by the weighted sum of squares of the wavefront aberration coefficients at respective points on the image plane (in the exposure region). In view of this, Japanese Patent Laid-Open No. 2005-268451 proposes a technique of optimizing a linear evaluation value (an optical characteristics value expressed by the linear function of the regulation amount of each element), and a quadratic evaluation value (an optical characteristics value expressed by the quadratic function of the regulation amount of each element) with a good balance for linear constraint expressions.
Japanese Patent Laid-Open No. 11-176744 and International Publication WO 02/054036 pamphlet propose other techniques associated with the regulation of the optical characteristics of the projection optical system.
For example, since a semiconductor device has various circuit patterns, the projection optical system is required to be regulated to maintain a satisfactory imaging performance for all of these various circuit patterns. It is therefore necessary to include, in an objective function for regulating the projection optical system, quadratic optical characteristics, such as the square of the RMS value of a wavefront aberration indicating the aberration in the entire region on the pupil plane of the projection optical system, which are expressed by the weighted sum of squares of the wavefront aberration coefficients at respective points in the exposure region, for example, the Zernike coefficients.
However, Japanese Patent Laid-Open Nos. 2002-367886 and 11-176744 and International Publication WO 02/054036 pamphlet do not take account of quadratic optical characteristics expressed by the weighted sum of squares of the wavefront aberration coefficients.
The projection optical system of the projection exposure apparatus generally has an exposure region as wide as about 26×8 [mm2]. To maintain a satisfactory imaging performance over the entire exposure region, the worst value of the optical characteristics in the exposure region is preferably taken into consideration. The technique disclosed in Japanese Patent Laid-Open No. 2005-268451 includes, in an objective function for regulating the optical system, quadratic optical characteristics expressed by the weighted sum of squares of the wavefront aberration coefficients. However, the technique disclosed in Japanese Patent Laid-Open No. 2005-268451 takes account of a quadratic optical characteristics value at one point in the exposure region, or the sum of quadratic optical characteristics values at a plurality of points in the exposure region. For this reason, the technique disclosed in Japanese Patent Laid-Open No. 2005-268451 cannot determine an optimum regulation amount that minimizes the worst value of the quadratic optical characteristics in the exposure region. Still worse, the technique disclosed in Japanese Patent Laid-Open No. 2005-268451 includes a process of determining a regulation amount that minimizes the linear evaluation value, and a process of determining a regulation amount that minimizes the quadratic evaluation value under constraints based on the processing result, and these processes must be repeated until the linear evaluation value and the quadratic evaluation value are balanced.